If they have shallow roots, pull them out. If they have deep roots, dig them out. Either needs to be done before they set seed. That's the only for-sure effective way, unfortunately. [There might be another way. See below.] It's hard to tell what particular weed is your one biggest offender here, but it seems to spread in patches. If you're lucky, you may be able to 'peel back' to just a few main root systems per patch, and pull them out. There are some kinds of weeds that will respond to more natural and less potent herbicides, but you need to know exactly what plant you're dealing with. With alternative options, 'Poison' to one weed can be 'Fertilizer' to another. And a lot of the "natural" herbicides useable for some weeds may work well or not at all depending on your local soil and climate. First, find out exactly what that main spreading weed is. Post close-ups. And/or post more detailed pictures at GardenWeb.com in the weeds forum. If you know a common name for the thing, Google it. When you know precisely what this main weed is, there might be other answers. Linda